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4.4 Exercises Do the exercises, and check your work. *Additional answers can be found in the Answers to Exercises appendix. Objective 1: Solve Problems Involving General Quantities Write a system of equations, and solve. 1) The sum of two numbers is 87, and one number is eleven more than the other. Find the numbers. 38 and 49 2) One number is half another number. The sum of the two numbers is 141. Find the numbers. 94 and 47 3) Through 2011, Harry Potter and the Deathly Hallows: Part 2 earned more money on its opening weekend in the United States than any other movie. It earned $100.8 million more than The Twilight Saga: Eclipse on its opening weekend. Together, they earned $237.6 million. How much did each fi lm earn on opening day? (http://boxoffi cemojo.com) Harry Potter: $169.2 million; Twilight: $68.4 million 4) In the 1976–1977 season, Kareem Abdul-Jabbar led all players in blocked shots. He blocked 50 more shots than Bill Walton, who fi nished in second place. How many shots did each man block if they rejected a total of 472 shots? (www.nba.com) Kareem: 261; Bill: 211 5) Through 2011, Beyonce had been nominated for four more BET Awards than Jay-Z. Determine how many nominations each performer received if they got a total of 54 nominations. (www.bet.com) Beyonce: 29; Jay-Z: 25 6) From 1965 to 2000, twice as many people immigrated to the United States from the Philippines as from Vietnam. The total number of immigrants from these two countries was 2,100,000. How many people came to the United States from each country? (www.ellisisland.org) Vietnam: 700,000; Philippines: 1,400,000 7) According to a U.S. Census Bureau survey in 2009, about half as many people in the United States spoke Vietnamese at home as spoke Chinese. If a total of about 3,900,000 people spoke these languages in their homes, how many spoke Vietnamese and how many spoke Chinese? (www.census.gov) Vietnamese: 1,300,000; Chinese: 2,600,000 8) During one week, a hardware store sold 27 fewer “regular” incandescent lightbulbs than energyeffi cient compact fl uorescent light (CFL) bulbs. How many of each type of bulb was sold if the store sold a total of 79 of these two types of lightbulbs? incandescent: 26; CFL: 53 9) On April 12, 1961, Yuri Gagarin of the Soviet Union became the fi rst person in space when he piloted the Vostok 1 mission. The next month, Alan B. Shepard became the fi rst American in space in the Freedom 7 space capsule. The two of them spent a total of about 123 minutes in space, with Gagarin logging 93 more minutes than Shepard. How long did each man spend in space? (www-pao.ksc.nasa.gov, www.enchantedlearning.com) Gagarin: 108 min; Shepard: 15 min 10) Mr. Monet has 85 students in his Art History lecture. For their assignment on impressionists, one-fourth as many students chose to recreate an impressionist painting as chose to write a paper. How many students will be painting, and how many will be writing papers? painting: 17; papers: 68 Objective 2: Solve Geometry Problems 11) Find the dimensions of a rectangular door that has a perimeter of 220 in. if the width is 50 in. less than the height of the door. width: 30 in.; height: 80 in. 12) The length of a rectangle is 3.5 in. more than its width. If the perimeter is 23 in., what are the dimensions of the rectangle? length: 7.5 in.; width: 4 in. 13) An iPod Touch is rectangular in shape and has a perimeter of 343.6 mm. Find its length and width given that it is 48.2 mm longer than it is wide. length: 110 mm; width: 61.8 mm 14) Eliza needs 332 in. of a decorative border to sew around a rectangular quilt she just made. Its width is 26 in. less than its length. Find the dimensions of the quilt. length: 96 in.; width: 70 in. 15) A rectangular horse corral is bordered on one side by a barn as pictured here. The length of the corral is 1.5 times the width. If 119 ft of fencing was used to make the corral, what are its dimensions? width: 34 ft; length: 51 ft 16) The length of a rectangular mirror is twice its width. Find the dimensions of the mirror if its perimeter is 246 cm. length: 82 cm; width: 41 cm 282 CHAPTER 4 Linear Equations and Inequalities in Two Variables www.mhhe.com/messersmith


messersmith_power_introductory_algebra_1e_ch4_7_10
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